A small container of water is placed on a carousel inside a microwave oven, at a radius of 13.5 cm from the center. The turntable rotates steadily, turning through one revolution each 6.90 s. What angle does the water surface make with the horizontal?
Im lost on how to do this question
To determine the angle at which the water surface makes with the horizontal, we need to consider the circular motion of the carousel and the given information.
Step 1: Calculate the linear speed of the water container.
The linear speed can be calculated using the formula:
v = 2πr / T
where v is the linear speed, r is the radius, and T is the time taken for one revolution.
Substituting the values:
r = 13.5 cm = 0.135 m
T = 6.90 s
v = (2π * 0.135) / 6.90
Using a calculator, find the value of v.
Step 2: Calculate the tangent of the angle.
The tangent of the angle can be found using the formula:
tanθ = v / g
where θ is the angle, v is the linear speed, and g is the acceleration due to gravity.
Substituting the respective values:
v = calculated in Step 1
g = 9.8 m/s^2 (approximate value for acceleration due to gravity)
Using a calculator, find the value of tanθ.
Step 3: Calculate the angle.
To find the angle θ, we can take the inverse tangent (arctan) of the previously calculated value of tanθ.
Using a calculator, find the value of θ.
The final value will be the angle at which the water surface makes with the horizontal.